Fission Products Experimental Programme: Validation and Computational Analysis Nicolas Leclaire*1, Tatiana Ivanova1, Eric Létang1, Emmanuel Girault2, Jean-François Thro3 1

Institut de Radioprotection et de Sûreté Nucléaire (IRSN), BP 17 92262 Fontenay-aux-Roses Cedex, France [email protected], [email protected], [email protected] 2 Commissariat à l’Energie Atomique (CEA), centre de Valduc – 21120 Is-sur-Tille, France [email protected] 3 AREVA NC 2, rue Paul Dautier 78000 Vélizy, France [email protected] *Corresponding author, Tel: +33 1.58.35.91.66, Fax: +33 1.46.57.29.98

Number of pages: 11 Number of Figures: 31 Number of Tables: 14

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Fission Products Experimental Programme: Validation and Computational Analysis Nicolas Leclaire, Tatiana Ivanova, Eric Létang, Emmanuel Girault, Jean-François Thro

Abstract – From 1998 to 2004 a series of critical experiments referred as the Fission Products (FP) experimental programme was performed at the Valduc research facility (CEA, France). The experiments were designed by IRSN, and funded by AREVA NC and IRSN within the French programme supporting development of a technical basis for burnup credit validation. The experiments were performed with the following six key fission products encountered in solution either individually or as mixtures: 133

Cs,

nat

Nd,

149

Sm,

152

Sm, and

155

103

Rh,

Gd. The programme aimed at compensating for the

lack of information on critical experiments involving fission products and at establishing a basis for fission products credit validation. 145 critical experiments have been performed, evaluated and analyzed with French CRISTAL criticality safety package and American SCALE5.1 code system employing different cross-section libraries. The aim of the paper is to show the experimental data potential to improve the ability to perform validation of full burnup credit calculation. The paper describes three phases of the experimental programme, the results of preliminary evaluation,

2

calculation, and sensitivity/uncertainty study of the FP experiments used to validate APOLLO2-MORET 4 route in CRISTAL criticality package for burnup credit applications.

3

I. INTRODUCTION In the 1980s, French nuclear reprocessing plants were designed taking into account the burnup of fissile materials. As far as burnup credit offers significant advantages for transport and storage, credit for reactivity change due to major actinides as the least value for 50-cm of the irradiated rod was adopted for criticality safety analysis. In recent years, need to handle and store higher quantities of fissile material led nuclear fuel managers to increase benefit of burnup credit by considering both the burnup profile and estimating a reactivity margin from the fission products in the safety design studies. To support the safety basis for the fission products credit validation, IRSN, on one side, investigated1 profit associated with burnup credit in the criticality safety evaluation for pressurized-water-reactor UOx spent nuclear fuel, and, on the other side, studied need of integral critical experiments involving fission products. As a consequence of that study, the key fission products accounting for approximately half of the total worth of all the fission products in irradiated fuel were selected2, and experimental programmes were performed to support validation of both actinide-only (HTCa programme3) and fission product credit. This paper describes 145 experiments referred to as the FP experiments, 73 of which were performed with the following fission products:

103

Rh,

133

Cs,

nat

Nd,

149

Sm,

152

Sm, and

155

Gd. Three phases of the

experimental programme are summarized in Table I: “Physical” (P), “Elementary Dissolution” (ED) and “Global Dissolution” (GD). This work contributes to the validation of APOLLO2-MORET 4 route of CRISTAL V1 criticality package4 for burnup credit calculation.

a

“Haut Taux de Combustion” experiments with rods having U and Pu isotopic composition similar to U(4.5%)O2 fuel with burnup of 37.5 GWd/MTU.

4

II. EXPERIMENTAL INSTALLATION The FP experimental programme was conducted at the Apparatus B in CEA/Valduc research center. The experimental device, shown in Fig. 1, is commonly used for assembling the configurations with epithermal and thermal neutron energy spectra. Flexibility of the installation provided easy assembling of the FPs configurations for each phase of the programme.

II.1. Apparatus B The Apparatus B presented in Fig. 1 consisted of a parallelepiped-shaped reflector pool, which is approximately centered in a large room of 12.1 x 8.8 x 10 m3 with concrete walls, floor, and ceiling. The pool had inner dimensions of 189.7 × 189.7 × 140 cm3 for “Physical” type configurations and 140 × 120 cm2 × 148.8 cm3 for “Elementary Dissolution” and “Global Dissolution” experiments. The 0.3-cm-thick pool walls and 0.6-cm-thick bottom were reinforced with girders. The fuel rods were installed into a basket, made of AG3Mb, which could contain a maximum of 2500 rods in a 50 x 50 array at 1.3-cm square pitch. The basket was supported by a stainless steel (Z2 CN 18.10) 2.5-cm-thick pedestal except “Physical” type experiments, for which the support was made of two joined plates with thicknesses of 1.0 cm and 2.5 cm. The pedestal was elevated above the reflector pool on 17.5, 33.7, and 42.3 cm for “Physical”, “Elementary Dissolution”, and “Global Dissolution” type configurations, accordingly. Variation of water or depleted uranyl nitrate (DUN) solution level in the tank accomplished the subcritical configuration within ≈0.1% from criticality.

Then the critical condition was linearly

extrapolated. This sub-critical approach procedure is illustrated in Fig. 2. b

Al alloy

5

A moderating solution gradually flooded the tank containing the fuels pin arrays. A side cylindrical well, communicating at the bottom with the pool tank, was equipped with a needle, which followed and measured a free upper level (H in Fig. 2) of the solution. The zero-level measurement was the bottom of the fuel column. Neutron counting rate (C in Fig. 2) was measured with six BF3 counters. Function 1/C = f(H) was extrapolated to determine the moderating solution critical level. Usually, the experiments were designed to provide the moderator height as close as possible to the fuel stack (90 cm). The reactivity was compensated by adding or removing fuel rods symmetrically in two or four peripheral rows in the initial square array.

II.2. UO2 and HTC rods To design and assembly the FPs configurations two types of simulated fuel rods in FP or non-FP solution were employed, depending on the programme’s phase: UO2 and HTC rods. The UO2 rods had a typical for pressurized-water reactor (PWR)

235

U enrichment of 4.738 wt.%.

The HTC rods were specifically designed for the HTC experimental programme to be similar to what would be found in a PWR fuel assembly that initially had an enrichment of 4.5 wt%

235

U and was

burned to 37.5 MWd/MTU. They were composed of (U-Pu)O2 (1.1 wt.% PuO2) with 1.57 wt.% enrichment and

240

Pu content was 24.333 wt.%. The HTC rods also included

241

235

U

Am. The principal

characteristics of the fuel rods are given in Table II (Uncertainties are indicated as 1σ). The UO2 and HTC rods are presented in Fig. 3. They consisted of pellets contained within Zircalloy 4 cladding and stuck together by means of a stainless steel spring. The rods diameter corresponded to the industrial fuel pin diameter. The fuel stack length adjusted to the dimension of the experimental tank was equal to 90 cm. The fuel rods were held in place by upper and lower grids placed into rectangular tank.

6

III. EXPERIMENTAL PROGRAMME The Fission Products experiments followed the Pré-FPs programme5 that had been carried out on the same facility before its renovation. The assembled configurations were similar to those for “Physical” type phase.

149

Sm nitrate solution was in the central tank surrounded by a driver array of UO2 rods in

AGS (aluminum alloy) clad. The precursor of the FPs programme was the first attempt to examine the absorption on 149Sm (top contributor to total worth of all FPs in irradiated fuels) and to have a clear idea of the experiments feasibility and accuracy associated with the FP solutions. The experience obtained has shown that such kind of experiments can be conducted to study burnup credit problems. Thus, series of 145 critical experiments referred to as the FP experiments was performed.

It

included the following three phases testing different interaction conditions between the fission products and the UO2 or the HTC rods (see Table I): 1. “Physical” type experiments dealt with the FPs presented individually or as mixture in low acidic solutions, without interaction with the fuel rods. 2. “Elementary Dissolution” type experiments dealt with the FPs presented individually or as mixtures in low acidic or depleted uranyl nitrate (DUN) solutions, interacting with array of the UO2 or the HTC rods. 3. “Global Dissolution” type experiments dealt with the mixture of FPs in DUN solutions, interacting with an array of the UO2 or the HTC rods. For each configuration, at least two experiments were conducted, one with and one without FP. The FPs concentration was chosen in order to reach a sufficient FP reactivity worth from 1.5% to 6%, depending on the FP. The following restrictions were taken into consideration: solubility limit for

7

133

Cs and

nat

Nd (130 g/l and 177 g/l, respectively) and available quantity of

solutions were not systematically pure. Namely, 155

Gd did 1.2% of 157Gd.

152

152

Sm. In addition, the FPs

Sm contained a small amount (0.29%) of

149

Sm,

nat

Nd solution used in the experiments contained 12.18% of 143Nd. The latter

being the main absorber among Nd isotopes is of strong interest. The preparation of FPs solutions was a subject matter for the experimental programme.

The

desirable accuracy of the solutions’ characteristics was obtained thanks to the method employed by chemists.

III.1. “Physical” type experiments The first step of the FPs programme was 45 “Physical” type experiments with slightly acidic solutions (0.014 to 2 N) of FPs in Zircaloy central tank. This tank of 6.2×6.2-cm2 internal dimension and 0.15-cm thickness was located in the center of UO2 rods array. The system was moderated and reflected by water. This series comprised 32 experiments with the following FPs presented at different concentrations in solution both separately and in the mixture:

103

Rh,

133

Cs,

nat

Nd,

149

Sm,

152

Sm, and

155

Gd.

The

experiments without FP (13) and with boron solution (1) were also performed. Figures 4 and 5 demonstrate the picture and scheme of a “Physical” type configuration.

III.2. “Elementary Dissolution” type experiments The second phase, “Elementary Dissolution”, included 86 configurations performed with one FP or mixed FPs in slightly acidic solutions (around 1 N), in a central tank with internal dimension 14.2 × 14.2 cm2 made of Zircaloy and containing an array of 11 × 11 UO2 or HTC rods at 1.271-cm square pitch.

8

This tank is located in the center of a driver array of UO2 rods at 1.3-cm square pitch, moderated and reflected by water. Vertical slice through the “Elementary Dissolution” type configuration is presented in Fig. 6. This series of experiments can be categorized into two groups:


68 experiments with UO2 (54) or HTC (14) rods in the central tank in water solution with (35) or

without (33) the fission products,


18 experiments with UO2 (10) or HTC (8) rods in the central tank in DUN solution with (7) or

without (11) the fission products.

III.3. “Global Dissolution” type experiments The third phase performed within the framework of the programme was a series of 14 experiments referred to as “Global Dissolution” type. They were conducted to address needs for validation of resonance self-shielding calculation for uranium, plutonium, and americium. The configurations were assembled from a tank with the UO2 or HTC rods array. The main part of the tank was a parallelepiped box made of stainless steel with internal dimensions of 70.40 x 70.40 x 114.8 cm3, wall thickness of 0.6 cm, and base thickness of 2.0 cm. The rods were secured by upper and lower horizontal grids fastened to the tank walls. Two identical 0.4-cm thick grids with dimensions 70.2 x 70.2 cm2 were placed face to face at distance of 96.8 cm to fix rods vertically in array. Vertical slice through the “Global Dissolution” type configuration is presented in Fig. 7. The experiments of this phase may be categorized as follows:


7 configurations with a 23 × 23 or 26 × 26 array of UO2 fuel rods at 1.3-cm square pitch,

moderated and reflected by DUN solutions with concentrations of 300 gU/l and 100 gU/l;

9




7 configurations with a 44 × 44 array of HTC fuel rods at 1.6-cm square pitch, moderated by

DUN (300 gU/l and 92 gU/l), poisoned or not by FPs, and reflected by water. Reproducibility of “Global Dissolution” type experiments was examined by performing several experiments with solutions of each uranium concentration (92 gU/l and 300 gU/l).

IV. EVALUATION OF EXPERIMENTAL DATA The Pré-FPs programme6, the precursor of the described FP experimental programme, was evaluated on the basis of the experimental data issued with tolerances (especially for the rods, clads, etc). In 1994, during re-cladding of the UO2 rods, measurements were performed to obtain more precise information about the fuel pellets and the clad. As a consequence, the uncertainties associated with their dimensions were also defined more precisely. The new data of the dimensions’ measurements were then used for evaluation of the FP experiments. Sensitivity studies were performed to assess the impact of various experimental uncertainties upon the configuration reactivity in accordance with recommendation of the ICSBEP uncertainty guide5. The 3D APOLLO2-MORET 4 Monte Carlo computations were used to determine the sensitivity of the results to variation of geometrical and material data. The sensitivity study was also performed with twodimensional cylindrical geometries using the APOLLO2 discrete ordinate code. The reactivity changes produced by the above tools were adopted as the associated components of the keff uncertainty. A specific treatment was applied to impurities in the fissile material and the FPs. Namely, for the UO2 fuel, the detected and measured impurities were modeled while other impurities were omitted adding the uncertainties. The impurities in composition of the HTC fuel and the fission products have negligible impact to the overall uncertainty.

10

The principal components of the keff errors are shown in Table III for the three types of experiments along with the overall uncertainty, calculated as the square root from sum of squares of its individual components. It can be seen that the rods density, pellet diameters, oxide impurities in the UO2 rods, and the rod positioning have a paramount effect on the overall uncertainty while the specific uncertainties associated with the FPs solutions are very small. The measurements of the rods performed during their re-cladding and accurate method of the solution FPs preparation lead to small overall uncertainties: less than 0.1% for the first two phases (“Physical” and “Elementary Dissolution” types) and about 0.15% for phase 3 (“Global Dissolution” type).

The level of rigor associated with these experiments shows that they have a potential to

contribute to fission product credit validation, adding to the small number of experiments applicable to this purpose.

V. ANALYSIS OF THE EXPERIMENTS The benchmark-models of all the critical configurations have been used to validate APOLLO2MORET 4 calculational route, which is utilized in France for criticality calculations within CRISTAL criticality package. The APOLLO2 – MORET 4 validation procedure7 is conducted through a comparison of the computed keff results for a designed system with the experimental data. The area of applicability of the experimental data is defined on the basis of comparison of such systems characteristics as: fuel material, fuel form, neutron energy spectra, reflection and moderation conditions, heterogeneity, interaction, spectral characteristics similar to those presented in the ICSBEP Handbook, etc. For the design systems that fall inside the area of applicability of the experiments, the expected computational bias is

11

established through an expert judgment of the computation-to-experiment difference for all of the selected critical configurations. No bias is assumed if the calculated values do not exceed experimental results for more than three combined standard deviations, which are computed as follows: 2 σ = σ 2calculation + σ benchmark , where σ calculation is a statistical uncertainty associated with Monte Carlo method,

and σ benchmark is an error associated with the uncertainties encountered in the experimental data and derivation of the benchmark model. Before performing such an analysis for the FP configurations, the APOLLO2-MORET 4 results were compared with those obtained by TRIPOLI-4.38 reference route, which uses continuous energy cross sections based on the same evaluated nuclear data library. If observed, the discrepancy between the two results allows separating the modeling error originating from approximations adopted in the APOLLO2 multi-group code and the uncertainty due to cross-section data. The calculations of the FP experiments have been performed to complete the APOLLO2-MORET 4 validation database. The SCALE5.19 codes system widely used for criticality safety study has been also employed to take advantage of variety of the codes for the FP experiments analysis. The details of eigenvalue calculations are presented in the following sections. All the computational results for three phases are gathered in Tables IX-XIV.

12

V.1. Computations with the CRISTAL Package The French CRISTAL package allows performing criticality calculations in two ways: standard APOLLO2-MORET 4 route with multi-group cross sections and TRIPOLI-4 Monte Carlo reference route with its specific point-wise neutron data library. The “standard” calculation is run in two steps using the following codes:


APOLLO2 is a one-dimensional lattice code used for preparation of multi-group cross sections

in equivalent cell approximation.


MORET 4 is the 3D Monte Carlo code for neutron transport calculation. It uses macroscopic

homogenized, self-shielded cross sections generated by the APOLLO2 code.

Typically, each

calculation employed 1000 neutrons per generation and is run to achieve a precision of 0.0003 (about 3000 generations). The following 172-group cross-section libraries were used by the APOLLO2 code:


CEA93 V6 is the standard route library based on the JEF2.2 evaluation. All isotopes are

developed in P1 Legendre polynomials, except moderating elements (such as H2O) and heavy nuclides (U, Pu) developed at the 5th and 9th order, respectively.


CEA2003 library is based on JEFF3.1 evaluation. All isotopes are developed in P5 Legendre

polynomials.


ENDF/B-VI cross-sections library is derived from ENDF/B-VI.4 evaluation. All isotopes are

developed in P5 Legendre polynomials. The model used for the APOLLO2 calculations is a cell equivalent to a fissile rod in the array configuration. It is simulated by coaxial infinite cylinders representing the fuel rod, surrounded by those 13

modeling cladding and water in the cell. Output of the APOLLO2 code is macroscopic cross sections homogenized in the cell. Thus, the model for 3D neutron transport calculation with the MORET 4 is a set of homogenized zones corresponding to different cells. Fig. 8 shows a view of the model as generated by MORET 4 graphical user interface. The reference TRIPOLI-4 route is a continuous energy Monte Carlo code. It employs continuous energy cross sections derived from JEF2.2 or ENDF/B-VI.4 evaluated nuclear data files. For the reference calculation the models are prepared without simplifications. An example of X-Z cut of the TRIPOLI-4 model is presented in Fig. 9.

V.2. Computations with SCALE 5.1 Code System The detailed input files were created for calculations with SCALE 5.1 Version codes system using both ENDF/B-V or ENDF/B-VI.7 238-group cross sections. Fig. 9, generated using SCALE5.1, shows a model for “Elementary dissolution” experiments. The CSAS25 control module utilized BONAMI and CENTRM for cross-section processing and then called KENO-V.a for the Monte Carlo calculations. The unit cell cylindrical model that comprised fuel pellet, cladding and water was used to create a problem-specific shielded cross-section set for each calculation.

V.3. Computational Results The keff results are depicted in Figures 10 to 19, where the statistical uncertainty of Monte Carlo computations is given as 3σ. All the computation results are shown also numerically in Tables IX to XIV. Comparison of the APOLLO2-MORET 4 and TRIPOLI-4 results obtained with group- and pointwise JEF2.2 cross-sections libraries shows that the discrepancies associated with self-shielded cross-

14

section processing are quite small (0.2% in average). A slight overestimation of the APOLLO2MORET 4 results compared to the experiments is also highlighted. Study of performance of different cross-sections libraries (see Fig. 10-12, 16, and 17) and both codes and libraries (see Fig. 13-15, 18, 19) revealed the following conclusions.
Use of the ENDF/B-VI evaluation with the CRISTAL standard (APOLLO2-MORET 4) and reference (TRIPOLI-4) routes leads to under-predicting keff for “Physical” and “Elementary Dissolution” type experiments with UO2 and HTC (internal array) rods placed at 1.3-cm square pitch lattices.
However, for the “Global Dissolution” configurations with the HTC rods placed at 1.6-cm pitch in DUN solution with concentration of 300gU/l, the results show a good agreement regardless of the library used. For the systems with higher moderator-to-fission ratio, the absence of the typically observed difference can be explained by shift of the neutron spectrum to softer energy range where probability to avoid resonances capture increases.
Use of JEFF3.1 evaluation with APOLLO2-MORET 4 leads to statistically slightly higher multiplication factor than those based on JEF2.2 evaluation. The new evaluation of 238U cross sections adopted in JEFF3.1 library may cause such a tendency.
The SCALE5.1 results obtained with ENDF/B-VI.7 and ENDF/B-V based cross sections are coherent with TRIPOLI-4 results employing ENDF/B-VI.4 library (the results are not available in this paper). All the mentioned libraries calculate from 1.1 to 0.6% low for the experiments with 1.3-cmpitch lattice. This tendency has been already observed10 for ENDF/B-V results. The resonance data adopted in the libraries can have a significant effect on results for the under moderated systems like the FP configurations with a tight pitch.

15


The calculations of

103

Rh solutions with different codes and cross sections under-predict the keff

significantly for all the “Elementary Dissolution” assemblies while the results for the “Physical” type configurations obey the common tendency observed for all the FPs experiments. The computations with different codes and both point- and group-wise libraries prove that this problem is not caused by the cross-sections processing. Since the neutron spectra in “Physical” and “Elementary dissolution” type experiments are similar, a similar calculation-to-experiment difference is expected for the configuration of both series, which is not the case. Sensitivity study shows that 10% change in concentration could explain the above discrepancy. Concretion of

103

103

Rh

Rh on the fuel rods and tank

surface may lead to such a decrease of the solution concentration. This assumption makes sense given that chemical features of rare-earth elements stipulate such

103

Rh behavior. The investigations are in

progress to reveal an origin of the results deviation for the experiments with 103Rh.

VI. SENSITIVITY ANALYSIS The FPs programme was carried out with the aim to address evaluation of reactivity margins associated with the fission products. Since this can be assessed only if the eigenvalue of the experiments are sensitive enough to the FPs nuclear data, the FPs reactivity worth along with the keff sensitivity to the FPs atomic density have been investigated.

VI.1. Fission Products Reactivity Worth The fission products worth was calculated as the difference between results for configuration containing the FP and without it. The results of the computations with the KENO V.a (SCALE5.1) code and the APOLLO2-MORET 4 route are presented in Table IV. The FP worth provided by the two calculational routes demonstrates a quite good agreement despite different cross-sections libraries are used in the above tools.

16

To examine response of absorption on fission products to their concentration, calculations were performed with variation of FPs atomic density keeping it constant for remaining nuclides.

The

computational results for two experiments (2883 Elementary Dissolution (ED) and 2834 Physical (P) type) with 103Rh are presented in Fig. 20 along with eigenvalue sensitivity to 103Rh atomic density. The above values were computed with APOLLO2-MORET 4 route. Sensitivity coefficients were received with correlated sampling method by 1% variation of FPs atomic densities, remaining constant densities for other nuclides. Fig. 20 exhibits that the saturation is obtained when the sensitivity coefficient approaches zero, i.e. when

103

Rh concentration is up to 100 g/l. Thus, the range of FPs concentrations

examined in the solutions (for example, about 20, 40, and 50 g/l for 103Rh) is chosen far enough from the saturation limit. The worth of FPs in the mixtures was analyzed and presented in Tables V-VII for three configurations related to each sub-programme.

Statistical dispersion for both KENO V.a and

APOLLO2-MORET 4 results is about 40 pcm. The second column in the tables shows worth of every FP in order of their consecutive addition to the solution of the FP mixture. While the last columns represent the worth of equivalent quantity of the FP being independent in the solution. Since in the “Elementary” and “Global dissolution” type configurations, contribution of capture on the FPs to the total neutron balance (captured by

238

U) is smaller than in “Physical” type experiments, the

“independent” FP worth and those in the mixture do not differ much (see Tables VI and VII). The difference is observed for the “Physical” type configurations (see Table V) because the FPs affect distinctly the total capture process in the system.

VI.2. Fission Product Absorption Rate The normalized cumulated absorption rate is plotted versus energy in Fig. 21 for the six FPs tested in the “Elementary Dissolution” type experimental programme. The so-called normalized cumulated 17

absorption rate1 is used to determine and to observe dependency of absorption rate upon energy. It can be seen that

149

Sm,

155

Gd and

143

Nd absorb neutrons mainly in the thermal energy range;

103

Rh,

152

Sm,

and 133Cs do at higher energy.

VI.3. Sensitivity Coefficients The SCALE5.1 code system and the APOLLO2-MORET 4 route used for computation of sensitivity coefficients allow comparing perturbation and correlated sampling method, respectively. TSUNAMI-3D code implemented in the SCALE5.1 code system calculates the sensitivity coefficients using adjoint based 1st order linear perturbation theory11 as follows: s=

δk σ , where σ is the nuclear data parameter of interest. In this work, sensitivity coefficients ⋅ k δσ

were calculated as the percent change in the system keff for one percent total cross section change in every of 238 energy groups and isotope of interest. The energy-dependent sensitivity profiles were studied and compared for different types of experiments (see Figures 24-29). Integrated sensitivities have been calculated as sum of the 238-group coefficients. Following the recommendations given in the TSUNAMI-3D manual, the obtained results have been compared with the sensitivity coefficients from direct perturbation of atomic density using KENO V.a Monte Carlo code with ENDF/B-VI.7 based 238group cross sections. The APOLLO2-MORET 4 route was also used for sensitivity analysis. Monte Carlo perturbation in MORET 4 is based on the correlated sampling method12 that allows calculating simultaneously keff value and an effect of small perturbation of initial data on the eigenvalue. The atomic densities were perturbed in this study.

18

Then integrated sensitivities obtained by different ways have been compared. Fig. 22 depicts the results of SCALE5.1 computations with ENDF/B-VI.7 library for major actinides, hydrogen, and

133

Cs.

The sensitivities for fission products are small relatively to those for major actinides. This may require special approach to quantify the bias and its uncertainty associated with the fission products credit. Table VIII and Fig. 23 illustrates that three different calculations produce quite good agreement for all major actinides and fission products in the configurations of three types. The neutron-energy dependent sensitivity profiles for all the tested FPs are compared for “Physical” and “Elementary Dissolution” experiments. The profiles comparison is given in Fig. 24 to 29. The eigenvalues for the configurations are sensitive to the FP and major actinides total cross sections in thermal and resonance energy range.

VI.4. Use of experimental data in estimation bias associated with the fission products As shown in previous section, eigenvalue sensitivities to fission products cross-section data are little relative to other materials such as fuel and moderator (see Fig. 22). This requires special technique that would magnify the effect of the fission products for evaluation of specific bias in keff associated with their nuclear data. As it was mentioned, the FP experimental programme was planned and performed in such a way to have pairs of the configurations with and without fission product. Both experiments had similar arrays and same fuel rods, but different heights of moderating solution (because the FP negative reactivity was compensated by increase of the solution height). For every pair, the experimental reactivity (change in keff between the two systems) is equal to zero within the experimental uncertainty, i.e.

FP non −FP kbenchmark = kbenchmark = 1.0000

.

It makes possible to estimate

computational bias associated with fission products cross-section data as follows: ∆k = ∆k − ∆k FP

FP

non−FP

calc

calc

. Such

19

differences were calculated with the APOLLO2-MORET 4 route and 172-group JEF2.2 cross sections. Fig. 30 shows them for “Physical” type configurations. It can be seen that the computational biases vary between 0 and 0.3%, depending on the testing FP. The experimental uncertainty associated with difference between the FP and non-FP configurations includes such components, as the FP solutions concentration and density, and critical height of moderator, which in sum do not exceed 0.02% (see Table III). The eigenvalue sensitivities were calculated by TSUNAMI-3D for each pair of experiments. Then differences of the sensitivities at the two states for some pairs of the experiments were calculated. As an example, sensitivities differences profiles for “Physical” dissolution configurations with and without 133

U fission and

238

U

Cs capture, while keff sensitivities to

235

U

Cs are depicted in Fig. 31. For the change in keff between the two cases, the

capture sensitivities are noticeably smaller than that for fission and

238

133

235

U capture shown in Fig. 22 and Table VIII are approximately an order of magnitude

greater than that of 133Cs capture. For the “Elementary dissolution” type configurations the

235

U sensitivities for keff differences are

higher and have the same order of magnitude as the FP sensitivities. This might be caused by greater differences between the FP and non-FP solution critical heights than those for “Physical type” experiments. Since the FP sensitivities can no longer be magnified experimentally by, for example, variation of the fuel rods number on the core periphery instead of the critical height of moderated solution, the calculational way to do this will be investigated. Preliminary analysis of the calculated bias, experimental uncertainty, and sensitivities for difference between the experiments with and without testing fission products has shown potential to magnify the effect of the tested materials. Work is planned to estimate bias due to fission products cross-section data for a burnup test application system employing the above values for Sensitivity/Uncertainty analysis 20

based on Generalized Linear Least Square Methodology13. This may allow fully taking advantage of the valuable information provided by the FP experimental programme.

CONCLUSION 145 critical experiments, presented in the paper, were conducted at the Valduc research facility to support fission products credit validation. The following six key fission products were studied within three phases of the programme: 103Rh, 133Cs, natNd, 149Sm, 152Sm, and 155Gd. The benchmark models of the experimental configurations were created.

The uncertainties of

experimental data were assessed using guidance of the ICSBEP. Since the experiments were performed with high level of rigor - the accurate data for the fission products solutions were provided by experimentalists, along with the new measurements, performed during UO2 rods re-cladding - the resulting experimental keff uncertainties do not exceed 0.15%. That allows using FP configurations as criticality benchmarks, adding to the previously small number of experiments applicable to assess FP credit. All the configurations were modeled using the French CRISTAL V1.1 package and American SCALE5.1 code system developed for criticality calculation.

The performance of the two codes

employing several cross-sections libraries was compared. The results of both standard and reference routes show a good agreement and tend to slightly over predict (except for 103Rh) the keff when using the CRISTAL V1.1 package with JEF2.2 based nuclear data. While SCALE5.1 with both ENDF/B-V and ENDF/B-VI.7 based cross sections tends to under predict keff. The origin of these tendencies can be mainly attributed to 235U and 238U cross section data10 in the employed libraries. Study of keff sensitivity to atomic density (total cross section) for major actinides and the FPs was performed. Use of different codes for calculation of the sensitivity coefficients allowed testing their 21

capability and has shown a good agreement for the values obtained with correlated sampling method (MORET 4), the 1st order direct perturbation theory (TSUNAMI-3D), and a direct perturbation for the majority of the cases. The sensitivity analysis exhibited that the sensitivity coefficients for the FPs are quite small compared to those for major actinides.

This will most likely create necessity to use

Sensitivity/Uncertainty analysis not for keff but for keff-difference to magnify the effect of the fission products and to predict bias and the bias uncertainty associated with their cross-section data. Work is planned to validate fission product credit calculation against the results of the presented experimental programme.

22

REFERENCES 1.J. Anno et al., “Planned Experimental Programme Qualifying the Safety Margins given by 6 Selected Fission Products in Spent Fuels”, Proc. Criticality Safety Challenges in the Next Decade, Chelan, 1997, 271 (1997). 2.J. Raby, C. Lavarenne, A. Barreau, Ph. Bioux, M. Doucet, E. Guillou, G. Léka, C. Riffard, B. Roque, H. Toubon, “Current studies related to the use of Burnup Credit in France”, Proc. ICNC2003, Tokaï, 2003. 3.F. Fernex, E. Girault, S. Evo; E. Letang, “High burnup experimental programme”, Proc. ANS 2006 summer meeting, Reno, 2006. 4.J.M. Gomit, P. Cousinou, Cheikh Diop, G. Fernandez de Grado, F. Gantenbein, J.P. Grouiller, A. Marc, D. Mijuin and H. Toubon, “CRISTAL V1: criticality package for burnup credit calculations”, Proc. ICNC2003, Tokaï, 2003. 5.International Handbook of Evaluated Criticality Benchmark Experiments NEA Nuclear Science Committee, NEA/NSC/DOC (95)03 – September 2007 Edition 6.J. Anno et al., “LEU-COMP-THERM-050.

149

Sm solution tank in the middle of water-moderated

4.738-wt.%-enriched uranium dioxide rods arrays”, ICSBEP Handbook, Sept. 2005. 7.N. Leclaire, I. Duhamel, E. Gagner, Y. K. Lee, C. Venard, “Experimental Validation of the French CRISTAL V1 package”, Proc. NCSD2005, Knoxville, 2005. 8.Y.K. Lee, E. Gagnier, L. Aguiar, N. Vedrenne, “Validation of the 3D Transport Monte Carlo Code TRIPOLI-4.3 for Moderated and Unmoderated Metallic Fissile Configurations with JEF2.2 and ENDF/B-VI.4 Cross Section Evaluations”, Proc. ICNC2003, Tokaï, 2003. 9.SCALE: A Modular Code System for Performing Standardized Computer Analyses for Licensing Evaluations, NUREG/CR-0200, Rev. 7 (ORNL/ NUREG/CSD-2/R7), Vols. I, II, and III (May 2004)

23

(Draft). Available from Radiation Safety Information Computational Center at Oak Ridge National Laboratory as CCC-725. 10. S. M. Bowman, W. C. Jordan, J. F. Mincey, C. V. Parks, L. M. Petrie, ORNL, “Experience With the SCALE Criticality Safety Cross-Section Libraries”, NUREG/CR-6686, ORNL/TM-1999/322, October 2000. 11. B. T. Rearden, "Perturbation Theory Eigenvalue Sensitivity Analysis with Monte Carlo Techniques," Nucl. Sci. Eng. 146, 367-382 (2004). 12. J. Anno, O. Jaquet, J. Miss, Validation of MORET 4 Perturbation against “Physical” Type Fission Products Experiments, Proc. ICNC2003, Tokaï, 2003. 13. B. L. Broadhead, "Application of Generalized Linear Least-Squares Methodology to Criticality Safety Computations," ANS 1997 Winter Meeting and Embedded Topical Mtgs., Albuquerque, NM, November 16-20, 1997.

VII. ACKNOWLEDGMENTS The authors wish to thank AREVA NC, who supports the Fission Product experimental programme and allowed publication of the results.

24

FOOTNOTES IN THE TEXT a

“Haut Taux de Combustion” experiments with rods having U and Pu isotopic composition similar to U(4.5%)O2 fuel with burnup of 37.5 GWd/MTU. b Al alloy

25

Fig. 1. Apparatus B.

26

Water height measurement system H FP sol.or DUN or HNO3 levelmeter 1/C

0

keff = F(H)

H

Clamp FP solution upper level Pilot lattice Uo2 Rod Pilot lattice fissile zone upper limit

When H HC 1/C 0 C = C0/(1-keff) Counting rate, C

HC

Zr tank containing the FP solution and the intern array UO2 or HTC Pilot lattice fissile zone lower limit

Neutron counters

Support

Water input and output Brace with input and output of the FP solution, or acid solution or DUN solution For each water height H, the neutron counting rate depends on the Keff = f(H). When the Keff increases and tends to 1, 1/C decreases and tends to 0. Thus, the intersection with the tangent abscissa axis to the curve 1/C = F(H) at the last measurement point determines the critical height Hc.

Fig. 2. Sub-critical approach technique.

27

0.95 cm

0.949

Top plug Zr4 102 cm

1.1 cm

Zircaloy-4 plug 1.468

Spring

9.1 cm

9.049

Spring Steel 39 spires 0.13 cm diameter Clad Zr4 0.95 cm outside diameter 0.064 cm thick

UO2 rods 102.082

4,738 % 235U

90.0 cm

φ = 0.789

Pellet 0.794 cm diameter

89.765 Zircaloy 4 clad Φext = 0.949 Φint = 0.836

1.8 cm

Bottom plug Zr4

Zircaloy 4 Plug

1.8

Dimensions in centimeters

0.0 cm

(a)

(b)

Fig.3. HTC (a) and UO2 (b) rods.

28

AG3M Plate

Central Tank (Zircaloy) Internal Dimensions 6.2 x 6.2 x 92.7 cm Thickness 0.15 cm 1.2 8.3

AG3M grid

Solution (FP, Boron or HNO3) H = 91 cm

0.4

96.5

130.4

1.2

“Zero” 3.5 Level

24

17.5 Dimensions in cm

Water 95 Drawing not to scale

Fig. 4. Scheme of “Physical” type experimental configuration (vertical cut).

29

Fig. 5. “Physical” type experimental installation.

30

Thick. 0.16 Upper GridHole diam. 0.98 Square Pitch 1.3

44.7

(Acidic or DUN solution) with or without FPs 104.6

93.80 98.8 89.765 95.0

Critical Height

Lower Grid Hole diam. 0.98 Square Pitch 1.3

160.1

2.5

“Zero” level

14.35 Water

36.2 80.0 Dimensions in cm

Drawing not to scale

Fig. 6. Scheme of “Elementary Dissolution” type experimental configuration (vertical cut).

31

Upper Grid Hole diam. 0.98 Square Pitch 1.6

(DUN) with or without FPs

112.8

90.0 95.0 96.8

DUN critical Height

70.4

170

Thick. 0.60

Lower Grid Hole diam. 0.98 Square Pitch 1.6 “Zero” level

2.0 Water

44.0 140.0

Thick. 0.50

Fig. 7. Scheme of “Global Dissolution” type experimental configuration (vertical cut).

32

Fig. 8. Half of the homogenized model (Vertical cut) for computation with the MORET 4 code.

33

Fig. 9. Heterogeneous model (Vertical cut) for computation with TRIPOLI-4 and SCALE 5.1.

34

1.012 1.01 1.008 1.006 1.004

1 0.998 0.996 0.994

APOLLO2-MORET 4 - JEF2.2

0.992

APOLLO2-MORET 4 - ENDF/B-VI.4

0.99

APOLLO2-MORET 4 - JEFF3.1

0.988

103Rh 103Rh 103Rh 103Rh 133Cs 133Cs 133Cs 133Cs 133Cs 133Cs 133Cs 133Cs 133Cs 133Cs Ndnat* Ndnat* 152Sm 152Sm 152Sm 152Sm 152Sm 155Gd 155Gd 155Gd 155Gd 155Gd Mixt. Mixt. Mixt. 149Sm 149Sm

keff

1.002

Fig. 10. keff for “Physical” type experiments. Library effect.

35

1.012 1.01 1.008 1.006 1.004

keff

1.002 1 0.998 0.996 0.994

APOLLO2-MORET 4 - JEF2.2 APOLLO2-MORET 4 - ENDF/B-VI.4 APOLLO2-MORET 4 - JEFF3.1

0.992 0.99

Fig. 11. keff for “Elementary Dissolution” type experiments (UO2 rods in central tank). Library effect.

36

Boron

Boron

Mixt3

Mixt3

Mixt2

Mixt2

Mixt1

Mixt1

155Gd

155Gd

155Gd

152Sm

152Sm

149Sm

149Sm

149Sm

149Sm

149Sm

143Nd

143Nd

103Rh

103Rh

103Rh

103Rh

103Rh

133Cs

133Cs

133Cs

133Cs

133Cs

0.988

1.012 1.01 1.008 1.006 1.004 K eff

1.002 1 0.998 0.996 0.994

APOLLO2-MORET 4 - JEF2.2 APOLLO2-MORET 4 - ENDF/B-VI.4 APOLLO2-MORET 4 -JEFF3.1

0.992 0.99

Mix t4

149Sm

149Sm

155G d

155G d

103R h

103R h

0.988

Fig. 12. keff for “Elementary Dissolution” type experiments (HTC rods in central tank). Library effect.

37

1.012 1.01 1.008 1.006

APOLLO2-M ORET 4 - JEF2.2 TRIPOLI4 - JEF2.2 SCALE5.1 - ENDF/B-VI.r7 SCALE5.1 - ENDF/B-V

1.004

keff

1.002 1

0.998 0.996 0.994 0.992 0.99 103Rh 103Rh 103Rh 103Rh 133Cs 133Cs 133Cs 133Cs 133Cs 133Cs 133Cs 133Cs 133Cs 133Cs Ndnat* Ndnat* 152Sm 152Sm 152Sm 152Sm 152Sm 155Gd 155Gd 155Gd 155Gd 155Gd Mixt. Mixt. Mixt. 149Sm 149Sm

0.988

Fig. 13. keff for “Physical” type experiments. Code and library effect. *142Nd was not available for the APOLLO2 computations. TRIPOLI-4 results have shown that its impact can be neglected.

38

1.012 APOLLO2-M ORET 4 - JEF2.2 TRIPOLI4 - JEF2.2 SCALE5.1 - ENDF/B-VI.r7 SCALE5.1 - ENDF/B-V

1.01 1.008 1.006 1.004

keff

1.002 1 0.998 0.996 0.994 0.992 0.99

Boron

Mixt3

Mixt2

Mixt1

155Gd

152Sm

149Sm

149Sm

149Sm

143Nd

103Rh

103Rh

133Cs

133Cs

133Cs

0.988

Fig. 14. keff for “Elementary Dissolution” experiments (UO2 rods in central tank). Codes and library effect.

39

1.012 1.01

APOLLO2-M ORET 4 - JEF2.2 TRIPOLI4 - JEF2.2 SCALE5.1 - ENDF/B-VI.r7 SCALE5.1 - ENDF/B-V

1.008 1.006 1.004

keff

1.002 1 0.998 0.996 0.994 0.992 0.99 Mixt4

149Sm

149Sm

155Gd

155Gd

103Rh

103Rh

0.988

Fig. 15. keff for “Elementary Dissolution” type experiments (HTC rods in central tank). Codes and library effect.

40

1.012

300 g/l

1.01

100 g/l

1.008 1.006 1.004

keff

1.002 1 0.998 0.996 0.994

APOLLO2-MORET 4 - JEF2.2 0.992

APOLLO2-MORET 4 - ENDF/B-VI.4 APOLLO2-MORET 4 - JEFF3.1

0.99 0.988

2967

2968

2969

2970

2971

2972

2973

Experiment Number

Fig. 16. keff for “Global Dissolution” (UO2 rods in DUN solution). Library effect.

41

1.012 1.01 1.008 1.006 1.004

keff

1.002 1

0.998

300 g/l

92 g/l

0.996 0.994

APOLLO2-MORET 4 -JEF2.2

0.992

APOLLO2-MORET 4 - ENDF/B-VI.4 APOLLO2-MORET 4 - JEFF3.1

0.99 0.988 2974

2975

2976

2977

2978

2979

2980

Experiment Number

Fig. 17. keff for “Global Dissolution” experiments (HTC rods in a DUN +FPs solution). Library effect.

42

1.012 1.01

300 g/l

100 g/l

1.008 APOLLO2-M ORET 4 - JEF2.2 TRIPOLI4 -JEF2.2 SCALE5.1 - ENDF/B-VI.r7 SCALE5.1 - ENDF/B-V

1.006 1.004

keff

1.002 1

0.998 0.996 0.994 0.992 0.99 0.988 2967

2968

2969

2970

2971

2972

2973

Experiment Number

Fig. 18. keff for “Global Dissolution” type experiments (UO2 rods in DUN solution). Code and library effect

43

1.012 1.01

92 g/l

300 g/l

1.008 1.006 1.004

keff

1.002 1 0.998 0.996 0.994

APOLLO2-MORET 4 -JEF2.2 TRIPOLI4 - JEF2.2 SCALE5.1 - ENDF/B-VI.r7 SCALE5.1 - ENDF/B-V

0.992 0.99 0.988 2974

2975

2976

2977

2978

2979

2980

Experiment Number

Fig. 19. keff for “Global Dissolution” experiments (HTC rods in DUN + FPs solution). Code and library effect.

44

26

0.035 Worth - P type (2834) Worth - ED type (2925) Sensitivity - P type (2834) Sensitivity - ED type (2925)

0.030 0.025

16

0.020 0.015

11

0.010

Sensitivity (%/%)

103

Rh worth (%)

21

6 0.005 1

0.000

0

50

100

150

200

250

300

350

400

450

500

Concentration (g/l)

Fig. 20.

103

Rh worth and eigenvalue sensitivity to 103Rh atomic density vs FP concentration.

45

Normalized cumulated absorption rate

1.E+00 9.E-01

103Rh 133Cs

8.E-01

143Nd 152Sm 149Sm

7.E-01 6.E-01

155Gd

5.E-01 4.E-01 3.E-01 2.E-01 1.E-01 0.E+00 1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

Energy, MeV

Fig. 21. Fission Products Cumulated Absorption Rate in a mixture.

46

0.350 0.300 0.250 0.200

GD type

ED type

0.150 0.100 0.050 0.000 -0.050

TSUNAMI-3D integral sensitivity (ENDF/B-VI evaluation) SCALE5.1 (ENDF/B-VI evaluation) direct perturbation

-0.100

240Pu

239Pu

238U

1H

235U

133Cs

238U

1H

235U

103Rh

133Cs

238U

1H

235U

103Rh

-0.150 133Cs

∆ K eff (%)

P type

Fig. 22. Integrated sensitivity coefficients for major actinides, hydrogen, 103Rh and 133Cs.

47

Mixture - Global Disso

Sm149

Sm149

Rh103

Gd155

Mixture 1

Mixture 1

Gd155

Gd155

Sm152

Sm149

Sm149

Ndnat

Rh103

Rh103

Rh103

Cs133

Sm149

Sm149

Mixture

Gd155

Gd155

Sm152

Sm152

Ndnat

Cs133

Cs133

Cs133

Cs133

Rh103

Rh103 0.000 -0.005 -0.010

Sensitivity (%/%)

-0.015 -0.020 -0.025 -0.030

PHYSICAL

-0.035 -0.040 -0.045

APOLLO2-MORET 4 ELEMENTARY DDISSOLUTION

TSUNAMI-3D (SCALE5.1) SCALE5.1 - direct perturbation

-0.050 Fission Product

10000 Sensitivity for P type (2834) Sensitivity for ED type (2925) Total cross section

-0.010

1000 -0.020

-0.030

100

-0.040

Cross section, barn

Sensitivity per unit of lethargy (%/%)

0.000

1.E+06

1.E+05

1.E+04

1.E+03

1.E+02

1.E+01

1.E+00

1.E-01

1.E-02

1.E-03

1.E-04

1.E-05

Fig. 23. Fission products: integrated sensitivities for three types of experiments.

10 -0.050

-0.060

1 Energy, eV

Fig. 24. 103Rh: Total cross section and sensitivity profiles for physical and elementary dissolution type experiments.

48

1.E+06

1.E+05

1.E+04

1.E+03

1.E+02

1.E+01

1.E+00

1.E-01

1.E-02

1.E-03

1.E-04

1.E-05

10000

-0.005 -0.01

1000

-0.015 -0.02 -0.025

100

-0.03 -0.035 -0.04 -0.045 -0.05

10 Sensitivity for P type (2809) Sensitivity for ED type (2875) Total cross section

Cross section, barn

Sensitivity per unit of lethargy (%/%)

0

1

Energy, eV

Fig. 25. 133Cs: total cross section and sensitivity profiles for physical and elementary dissolution type experiments.

49

1.E+06

1.E+05

1.E+04

1.E+03

1.E+02

1.E+01

1.E+00

10000000

-0.002

1000000 Sensitivity for P type (2828) Sensitivity for ED type (2926) Total cross section

-0.004 -0.006

100000

-0.008

10000

-0.01

1000

-0.012

100

Cross section, barn

1.E-01

1.E-02

1.E-03

1.E-04

1.E-05 Sensitivity per unit of lethargy (%/%)

0

-0.014 10

-0.016 -0.018

1 Energy, eV

Fig. 26. 155Gd: Total cross section and sensitivity profiles for physical and elementary dissolution type experiments.

50

1.E+06

1.E+05

1.E+04

1.E+03

1.E+02

1.E+01

1.E+00

1.E-01

1.E-02

1.E-03

100000

-0.005

10000

-0.01

1000

-0.015

100

-0.02

10

Cross se ction, b arn

1.E-04

1.E-05 Se nsitivity pe r un it of le th arg y (%/%)

0

Sensitivity for P type (2823)

-0.025

Sensitivity for ED type (2901) Total cross section

-0.03

1

0.1 Energy, eV

Fig. 27. 152Sm: total cross section and sensitivity profiles for physical and elementary dissolution type experiments.

51

-0.005

Sensitivity for P type (2847)

1000000

Sensitivity for ED type (2897)

-0.01

Total cross section

100000

-0.015 10000 -0.02 1000 -0.025 100

-0.03 -0.035

10

-0.04

1

Cross section, barn

Sensitivity per unit of lethargy (%/%)

1.E+06

1.E+05

1.E+04

1.E+03

1.E+02

1.E+01

1.E-01

1.E-02

1.E-03

1.E-04

1.E-05

1.E+00

10000000

0

Energy, eV

Fig. 28. 149Sm: total cross section and sensitivity profiles for physical and elementary dissolution type experiments.

52

1 .E+0 8

1 .E+0 7

1 .E+0 6

1 .E+0 5

1 .E+0 4

1 .E+0 3

1 .E+0 2

1 .E+0 1

1 .E+0 0

1 .E-0 1

1 .E-0 2

1 .E-0 3

1 .E-0 4

1 .E-0 5

10000

-0.0005 -0.001

1000

-0.0015 -0.002

100

-0.0025 -0.003

10

-0.0035 -0.004 -0.0045

C r os s s e c tion , b ar n

S e n s itivity p e r u n it of le th ar g y (% /% )

0

1 Sensitivity for P type (2821) Sensitivity for ED type (2880) Total cross section

-0.005

0.1 Energy, eV

Fig. 29. 143Nd: total cross section and sensitivity profiles for physical and elementary dissolution type experiments.

53

0.4

103Rh

133Cs

149Sm

152Sm

155Gd

Nd

0.3

0.1

0.0

-0.1

-0.2

-0.3

2849

2847

2845

2843

2841

2839

2837

2835

2833

2831

2829

2827

2825

2823

2821

2819

2817

2815

2813

2811

2809

2807

-0.4 2805

keffFP-keffNo FP (%)

0.2

Experiment Number

Fig. 30. Fission Products bias for “Physical” type experiments (results of APOLLO2-MORET 4 computation with JEF2.2 based library)

54

Fig. 31. keff difference sensitivity for “Physical” type configurations with (#2809) and without (#2803) 133Cs

55

TABLE I Fission Products Experimental Programme Configurations Type Date Driver array in water Central tank Fuel rods → Solution ↓ Water + HNO3 Water + Boron FP solution Non FP 149

PHYSICAL ELEMENTARY DISSOLUTION (Nov 1998 (Sept. 2000 – (Sept. 2000 – June 1999) Nov. 2001) March 2002) 235 1.3-cm square pitch array of U(4.738 % U)O2 rods 23 × 21 to 27 × 27 14.35 × 14.35 cm2 2 with 1.271-cm square pitch array of 6.2 × 6.2 cm 235 U(4.738 % U)O2 or HTC rods UO2 UO2 N/A HTC HTC Number of experiments 13 26 7 8 3 1 Water + HNO3 2 2

5

2

4

5

2

Cs

10

5

Nd

2

2

5

2

5

3

2

Mixture

3

6

1

Sub-total Total General Total

45 45

54

Sm

103

Rh

133 nat

152

Sm

155

Gd

GLOBAL DISSOLUTION (Nov-Dec. 2003 and April 2004) UO2 rods HTC rods in 1.3-cm in 1.6-cm square pitch square pitch array array 26 x 26 or 44 × 44 23 x 23

14

Depleted Uranyl Nitrate (DUN) 2 7

3

1

2 10

68

8 18

4 7

7 14

145

56

TABLE II Characteristics of HTC and UO2 rods. Characteristic

Value

Density (g/cm3) Stoichiometry O/(U+Pu) (atomic ratio) Pu/(U+Pu) (wt. %) Outer clad diameter (cm) Fuel pellet diameter (cm) Isotope 234 U 235 U 236 U 238 U 238 Pu 239 Pu 240 Pu 241 Pu 242 Pu 241 Am

10.333

HTC rods 0.445

1.9971

0.005

Density (g/cm3) Stoichiometry O/U (atomic ratio) Outer clad diameter (cm) Fuel pellet diameter (cm) Isotope 234 U 235 U 236 U 238 U

1.104 0.94958 0.7940 Weight % 0.013 1.570 0.001 98.416 1.304 59.227 24.333 10.076 5.056 1.432 10.38

Uncertainty (1σ)

0.060 0.00058 0.0058 Uncertainty < 5.10-4 < 5.10-4 < 5.10-4 < 5.10-4 < 5.10-4 < 5.10-4 < 5.10-4 < 5.10-4 < 5.10-4 < 5.10-4 UO2 rods 0.22

2.000

0.001

0.94924 0.78919 Weight % 0.0302 4.7376 0.1362 95.0959

0.00044 0.00176 Uncertainty 0.0005 0.0020 0.0005 0.0010

57

TABLE III Major Contributors and Overall Maximum Experimental Uncertainty for “Physical” type, “Elementary Dissolution” type and “Global Dissolution” type Experiments Programme type

ELEMENTARY DISSOLUTION 1σ Uncertainty (%)

GLOBAL DISSOLUTION

0.010 0.025 0.031 0.025 0.011 0.025

0.033 0.025 0.035 0.025 0.023 0.025

0.005 0.025 0.058 0.005 0.007 0.132

0.012

0.012

0.003

0.034

0.020

0.006

0.016

0.020

0.008

0.001 0.001 0.067

0.006 0.001 0.075

0.010 0.001 0.147

PHYSICAL

Component of uncertainty ↓ UO2 and HTC rods Isotopic content Rods density Oxide impurities Pellet diameter Inner clad diameter Outer clad diameter Physical data Temperature Rods positioning (pitch + grid hole diameter) Critical height Fission Products Concentration Density Total

58

TABLE IV FPs Reactivity Worth Exp N° (Programme Type) 2835 (P) 2811 (P) 2817 (P) 2823 (P) 2826 (ED) 2828 (P) 2844 (P) 2847 (P) 2883 (ED) 2925 (ED) 2880 (ED) 2897 (ED) 2901 (ED) 2929 (ED) 2943 (ED) 2912 (ED) 2910 (ED) 2915 (ED) 2917 (ED) 2964 (ED) 2965 (ED) 2977 (GD)

FPs 103

Rh Cs 133 Cs 152 Sm 152 Sm 155 Gd Mixture 149 Sm 103 Rh 103 Rh nat Nd 149 Sm 152 Sm 155 Gd Mixture 155 Gd 103 Rh 149 Sm Mixture 149 Sm Mixture Mixture 133

C(FP) g/l 20 130 77 50 20 0.2 N/A 0.2 50 20 90 0.4 15 0.15 N/A 0.4 30 0.2 N/A 0.2 N/A N/A

FP worth (pcm) APOLLO2- KENO V.a/ MORET 4 SCALE5.1 1737 1766 2169 1980 1387 1278 4510 4332 3361 3112 2705 2752 2899 2923 3592 3496 6241 6177 3626 3677 1568 1677 6594 6470 3522 3376 3368 3286 3541 3593 3436 3430 3206 3171 3514 3539 3436 3444 2337 2228 2831 2777 4516 4281

* The FP concentrations have been rounded (protected data)

59

TABLE V FP Worth in “Physical” type Experiment #2844 FP 103

Rh Cs 155 Gd 149 Sm 152 Sm 143 Nd Total (All)) 133

FP worth in mixture (pcm) 783 617 469 658 122 150 2799

“Independent” FP worth (pcm) 783 623 671 993 192 338 3600

60

TABLE VI FP worth in “Elementary Dissolution” type Experiment #2943 FP 133

Cs Rh nat Nd 155 Gd 149 Sm 152 Sm Total (All) 103

FP worth in mixture (pcm) 638 808 196 657 708 543 3550

“Independent” FP worth (pcm) 638 791 211 687 732 593 3652

61

TABLE VII FP worth in “Global Dissolution” type Experiment #2977 FP 103

Rh Cs 155 Gd 149 Sm 152 Sm nat Nd Total (All) 133

FP worth in mixture (pcm) 140 1118 1020 1251 60 617 4206

“Independent” FP worth (pcm) 140 1175 1058 1318 61 694 4446

62

TABLE VIII keff Sensitivity for Nuclide Atomic Density or Total Cross Section (TSUNAMI-3D) (%/%) Exp. N° (Programm e Type) 2811 (P) 2834 (P) 2875 (ED) 2925 (ED) 2917 (ED) 2834 (P) 2925 (ED) 2977 (GD) 2834 (P) 2925 (ED) 2977 (GD) 2834 (P) 2925 (ED) 2977 (GD) 2977 (GD) 2977 (GD)

Isotope 133

Cs Rh 133 Cs 103 Rh 133 Cs 235 U 235 U 235 U 1 H 1 H 1 H 238 U 238 U 238 U 239 Pu 240 Pu 103

APOLLO2MORET 4 correlated sampling (uncertainty) -0.0144 (1) -0.01800 (5) -0.01992 (3) -0.02817 (4) -0.0040 (1) 0.1536 (3) 0.1616 (1) 0.1679 (1) -0.0736 (3) -0.0808 (2) -0.1198 (4) 0.1266 (4) -0.0432 (1)

SCALE5.1 direct perturbation (uncertainty)

TSUNAMI3D (uncertainty)

-0.0151 (2) -0.0183 (2) -0.0199 (2) -0.0265 (2) -0.0033 (2) 0.1551 (2) 0.1549 (2) 0.1658 (2) 0.2895 (2) 0.3143 (2) 0.1253 (2) -0.0691 (2) -0.0773 (2) -0.1165 (2) 0.1227 (2) -0.0442 (2)

-0.0139 (6) -0.0186 (7) -0.0209 (3) -0.0295 (3) -0.0039 (8) 0.1555 (5) 0.1541 (7) 0.1664 (3) 0.2911 (3) 0.3227 (3) 0.1297 (1) -0.0677 (6) -0.0666 (3) -0.1099 (9) 0.1229 (2) -0.0453 (3)

63

TABLE IX keff Results and FP Reactivity Worth for “Physical” Type Experiments (σcalc = 0.00030) Case

Rh Rh 103 Rh 103 Rh 133 Cs 133 Cs 133 Cs 133 Cs 133 Cs 133 Cs 133 Cs 133 Cs 133 Cs 133 Cs nat Nd nat Nd 152 Sm 152 Sm 152 Sm 152 Sm 152 Sm 155 Gd 155 Gd 155 Gd 155 Gd 155 Gd Mixt. Mixt.

APOLLO2-MORET 4 FP worth TRIPOLI-4.3 SCALE5.1 (pcm) JEF2.2 JEF3.1 ENDF/B-VI.4 JEF2.2 ENDF/B-VI.7 1.00300 1.00526 0.99855 3124 1.00000 0.99268 1.00363 1.00567 0.99966 2798 1.00109 0.99152 1.00331 1.00439 0.99867 1793 0.99887 0.99175 1.00266 1.00478 0.99762 1953 0.99919 0.99141 1.00176 1.00236 0.99800 2147 0.99907 0.99171 1.00029 1.00262 0.99812 2294 0.99895 0.99160 1.00104 1.00278 0.99770 2169 0.99990 0.99118 1.00091 1.00276 0.99775 1501 0.99914 0.99099 1.00079 1.00274 0.99794 1490 0.99777 0.99129 1.00206 1.00343 0.99723 1448 0.99910 0.99118 1.00183 1.00287 0.99857 1438 0.99918 0.99160 1.00255 1.00395 0.99781 1314 0.99929 0.99148 1.00150 1.00325 0.99856 1359 0.99945 0.99113 1.00154 1.00277 0.99766 1523 0.99894 0.99206 1.00402 1.00529 1.00078 1470 0.99948 0.99209 1.00404 1.00553 1.00088 1877 0.99907 0.99152 1.00109 1.00237 0.99780 4474 0.99987 0.99151 1.00073 1.00203 0.99722 4555 0.99843 0.99175 1.00154 1.00273 0.99736 4654 0.99901 0.99145 1.00161 1.00319 0.99793 3361 1.00042 0.99235 1.00196 1.00224 0.99830 3358 0.99932 0.99264 1.00259 1.00415 0.99883 2705 1.00118 0.99115 1.00256 1.00346 0.99862 2747 0.99899 0.99118 1.00167 1.00321 0.99817 2880 0.99967 0.99108 1.00287 1.00369 0.99825 1932 0.99800 0.99190 1.00331 1.00426 0.99871 1737 0.99851 0.99176 1.00294 1.00366 0.99981 2899 1.00000 0.99190 1.00296 1.00391 0.99870 0.99894 0.99169

Mixt.

1.00254

1.00395

0.99901

-

0.99963

0.99137

149

1.00198 1.00247 1.00332 1.00215 1.00108

1.00317 1.00370 1.00544 1.00391 1.00270

0.99865 0.99847 0.99953 0.99842 0.99758

3592 2246

0.99834 0.99903 1.00009 0.99819 0.99709

0.99198 0.99132 0.99045 0.99031 0.99031

Exp. C(FP)* g/l Solution N°

1 2 3 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

2833 2834 2835 2837 2805 2806 2811 2807 2808 2809 2810 2812 2817 2818 2821 2822 2823 2824 2825 2826 2827 2828 2829 2830 2831 2832 2844 2845

30

2846

31 32 34 35 36

2847 2848 2820 2803 2804

40 40 20 20 130 130 130 80 80 80 80 80 80 80 120 120 50 50 50 20 20 0.2 0.2 0.2 0.1 0.1 103 Rh 7 133 Cs 30 155 Gd 0.05 152 Sm 1.5 149 Sm 0.04 nat Nd 25 0.2 0.1 0.9

103 103

Sm Sm nat B HNO3 HNO3 149

* The real concentrations are close to the given values

64

TABLE IX (cont’d) keff Results and FP Reactivity Worth for “Physical” Type Experiments (σcalc = 0.00030) Case Exp. N° Solution 37 38 39 40 41 42 43 44 45 46 47

2813 2814 2815 2816 2838 2839 2840 2841 2842 2843 2849

HNO3 HNO3 HNO3 HNO3 HNO3 HNO3 HNO3 HNO3 HNO3 HNO3 HNO3

APOLLO2-MORET 4 ENDF/BJEF2.2 JEF3.1 VI.4 1.00280 1.00509 0.99910 1.00303 1.00446 0.99901 1.00241 1.00401 0.99942 1.00242 1.00472 0.99887 1.00320 1.00448 0.99914 1.00300 1.00413 0.99815 1.00341 1.00447 0.99860 1.00303 1.00418 0.99895 1.00283 1.00392 0.99831 1.00264 1.00426 0.99909 1.00295 1.00449 0.99874

TRIPOLI-4.3

SCALE 5.1

JEF2.2

ENDF/B-VI.7

0.99910 0.99964 0.99998 0.99888 0.99862 0.99903 0.99930 0.99981 0.99861 0.99970 0.99936

0.99072 0.99146 0.99202 0.99151 0.99148 0.99064 0.99130 0.99138 0.99151 0.99159 0.99194

65

TABLE X keff Results and FP Reactivity Worth for “Elementary Dissolution” Type Experiments – UO2 Rods in Central Tank (σcalc = 0.00030) Case 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

FP APOLLO2-MORET 4 Experiment Concentration* Solution worth N° (g/l) JEF2.2 JEFF3.1 ENDF/B-VI.4 (pcm) 133 2875 110 Cs 1.00397 1.00515 0.99990 2823 133 2876 110 Cs 1.00354 1.00443 1.00063 2777 133 2877 110 Cs 1.00265 1.00480 0.99986 2901 133 2878 110 Cs 1.00291 1.00377 0.99945 2876 133 2879 110 Cs 1.00307 1.00483 0.99944 2876 103 2883 50 Rh 0.99912 1.00205 0.99399 6241 103 2884 50 Rh 0.99935 1.00131 0.99482 6322 103 2923 20 Rh 0.99952 1.00109 0.99478 3399 103 2924 20 Rh 0.99886 1.00185 0.99426 3554 103 2925 20 Rh 0.99933 1.00100 0.99416 3626 nat 2880 90 Nd 1.00398 1.00464 0.99945 1568 nat 2881 90 Nd 1.00416 1.00479 1.00030 1599 149 2897 0.4 Sm 1.00426 1.00237 1.00054 6594 149 2898 0.4 Sm 1.00417 1.00220 1.00003 6502 149 2928 0.15 Sm 1.00188 1.00335 0.99812 3484 149 2929 0.15 Sm 1.00379 1.00275 0.99920 3368 149 2931 0.15 Sm 1.00237 1.00207 0.99851 3370 152 2901 15 Sm 1.00309 1.00386 0.99881 3522 152 2902 15 Sm 1.00323 1.00383 0.99895 3494 155 2900 0.8 Gd 1.00588 1.00620 1.00195 6933 155 2926 0.4 Gd 1.00388 1.00467 1.00008 3762 155 2927 0.4 Gd 1.00374 1.00417 0.99826 3805 2943 Mixt1 1.00294 0.99868 1.00380 3541 2944 Mixt1 1.00320 0.99943 1.00420 3652 2939 Mixt2 1.00548 1.00574 1.00226 7893 2940 Mixt2 1.00515 1.00515 1.00218 7894 2937 Mixt3 1.00706 1.00269 1.00581 7951 2938 Mixt3 1.00688 1.00242 1.00604 8003 HNO3 1.00193 1.00199 2872 0.99618 HNO3 1.00216 1.00271 2873 0.99624 HNO3 1.00228 1.00376 2885 0.99649 HNO3 1.00127 1.00209 2886 0.99556 HNO3 1.00134 1.00238 2887 0.99588 HNO3 1.00165 1.00189 2888 0.99594 HNO3 1.00104 1.00265 2889 0.99570 HNO3 1.00131 1.00172 2890 0.99574 HNO3 1.00119 1.00261 2891 0.99613 HNO3 1.00084 1.00274 2892 0.99637 HNO3 1.00154 1.00222 2893 0.99566 HNO3 1.00033 1.00120 2894 0.99547 HNO3 1.00027 1.00234 2895 0.99612 HNO3 1.00142 1.00229 2903 0.99618 HNO3 1.00065 1.00116 2904 0.99534 HNO3 1.00104 1.00202 2905 0.99647 HNO3 1.00062 1.00249 2932 0.99601

TRIPOLI-4.3

SCALE5.1

JEF2.2

ENDF/B-VI.7

1.00033 1.00137 1.00078 1.00069 0.99999 0.99619 0.99762 0.99723 0.99792 0.99664 1.00057 0.99800 1.00080 1.00091 1.00037 1.00124 1.00005 1.00139 1.00184 1.00342 1.00042 0.99693 1.00148 0.99985 1.00291 1.00749 1.00389 1.00363 0.99952 0.99927 0.99859 0.99936 0.99954 0.99874 0.99951 0.99901 0.99809 0.99803 0.99951 0.99855 0.99867 0.99949 0.99879 0.99878 0.99946

0.99291 0.99277 0.99279 0.99284 0.99264 0.98928 0.98862 0.98922 0.98907 0.98919 0.99227 0.99248 0.99393 0.99309 0.99149 0.99324 0.99205 0.99254 0.99312 0.99475 0.99262 0.99286 0.99141 0.99280 0.99487 0.99462 0.99573 0.99291 0.98563 0.99016 0.99017 0.98899 0.98950 0.98968 0.98933 0.98924 0.98952 0.98952 0.98872 0.99155 0.98766 0.98945 0.98656 0.98793 0.98933

66

* The real concentrations are close to the given values TABLE X (cont’d) keff Results and FP Reactivity Worth for “Elementary Dissolution” Type Experiments – UO2 Rods in Central Tank (σcalc = 0.00030) Case 48 49 50 51 52 53 54

APOLLO2-MORET 4 TRIPOLI-4.3 SCALE5.1 Experiment Solution N° JEF2.2 JEFF3.1 ENDF/B-VI.4 JEF2.2 ENDF/B-VI.7 HNO3 1.00131 1.00216 2933 0.99819 0.98964 0.99658 HNO3 1.00101 1.00256 2934 0.99787 0.98990 0.99694 HNO3 1.00146 1.00198 2936 0.99880 0.98807 0.99677 HNO3 0.99976 1.00064 0.98597 1.00004 2941 0.99400 HNO3 1.00027 1.00165 0.98592 0.99829 2942 0.99439 HNO3 1.00129 1.00176 0.99850 0.98922 2951 0.99593 HNO3 1.00153 1.00255 1.00031 0.98980 2952 0.99643

67

TABLE XI keff Results and FP Reactivity Worth for “Elementary Dissolution” Type Experiments – HTC Rods in Central tank (σcalc = 0.00030) Case 55 56 57 58 59 60 61 62 63 64 65 66 67 68

FP Experiment Concentration* Solution worth N° (g/l) (pcm) 103 30 2910 Rh 3238 103 30 2911 Rh 3169 155 0.4 2912 Gd 3369 155 0.4 2913 Gd 3437 149 0.2 2915 Sm 3509 149 0.2 2916 Sm 3556 2917 Mixt4 3457 2906 HNO3 HNO3 2907 HNO3 2908 HNO3 2918 HNO3 2919 HNO3 2920 HNO3 2921

APOLLO2-MORET 4

TRIPOLI-4.3 SCALE5.1

JEF2.2

JEFF3.1 ENDF/B-VI.4

JEF2.2

ENDF/B-VI.7

0.99936 0.99913 1.00368 1.00241 1.00227 1.00243 1.00250 1.00128 1.00074 1.00024 1.00082 1.00129 1.00094 1.00136

1.00306 1.00112 1.00443 1.00379 1.00299 1.00245 1.00342 1.00266 1.00224 1.00278 1.00185 1.00239 1.00147 1.00299

0.99931 0.99721 1.00127 1.00038 1.00134 1.00094 1.00072 0.99995 0.9992 1.00021 1.00018 1.00035 0.99964 0.99974

0.98991 0.99001 0.99379 0.99326 0.99265 0.99290 0.99377 0.99214 0.99214 0.99077 0.99045 0.99050 0.99042 0.99071

0.99584 0.99484 0.99906 0.99901 0.99840 0.99898 0.99939 0.99765 0.99650 0.99671 0.99571 0.99602 0.99643 0.99663

* The real concentrations are close to the given values

68

TABLE XII keff Results and FP Reactivity Worth of “Elementary Dissolution” Type Experiments – UO2 Rods in DUN Solution in the Central Tank (σcalc = 0.00030) Case Experiment N° 1 2 3 4 5 6

2960 2961 2962 2963 2964 2965

7

2966

Concentration* (g/l) 396 396 396 396 395/0.2 (Sm) DUN 125 103 Rh 3 133 Cs 15 nat Nd 15 149 Sm 0.05 152 Sm 3 155 Gd 0.05

TRIPOLI4.3f ENDF/B-VI.4 JEF2.2

SCALE5.1

FP worth (pcm)

JEF2.2

JEFF3.1

DUN-1 DUN-1 DUN-2 DUN-2 DUN+Sm 2291 Mixt5 2841

1.00295 1.00325 1.00186 1.00180 1.00304 1.00240

1.00404 1.00359 1.00323 1.00255 1.00347 1.00417

0.99839 0.99759 0.99724 0.99782 0.99952 0.99960

1.00152 1.00051 1.00097 1.00120 1.00126 1.00226

0.99240 0.99269 0.99288 0.99305 0.99450 0.99380

1.00349

1.00426

0.99947

1.00146

0.99411

Solution

Mixt5

2730

APOLLO2-MORET 4

ENDF/B-VI.7

* The real concentrations are close to the given values

69

TABLE XIII keff Results and FP Reactivity Worth for “Global Dissolution” Type Experiments – UO2 Rods in DUN Solution. (σcalc = 0.00030) Case 1 2 3 5 6 7 8

Experiment C(DUN)* N° (g/l) 2967 2968 2969 2970 2971 2972 2973

300 300 300 92 92 92 92

Solution DUN DUN DUN DUN DUN DUN DUN

APOLLO2-MORET 4

TRIPOLI-4.3

SCALE5.1

JEF2.2

JEFF3.1

ENDF/B-VI.4

JEF2.2

ENDF/B-VI.7

0.99999 1.00114 1.00165 1.00202 1.00136 1.00143 1.00100

1.00103 1.00215 1.00179 1.00206 1.00275 1.00264 1.00187

0.99479 0.99703 0.99638 0.99662 0.99613 0.99604 0.99626

0.99699 0.99645 0.99573 0.99884 0.99812 0.99906 0.99833

0.99010 0.99023 0.99070 0.99090 0.99080 0.99169 0.99051

* The real concentrations are close to the given values

70

TABLE XIV keff results and FP reactivity worth for “Global Dissolution” type experiments – HTC rods in a uranyl nitrate solution with or without FP. (σcalc = 0.00030) Case 1 2 3 4 5 6 7

Experiment N°

C(DUN)* g/l

Solution

2974 2975 2976 2977 2978 2979 2980

300 300 300 92 92 92 92

DUN DUN DUN Mixt. Mixt. Mixt. Mixt.

FP worth (pcm)

APOLLO2-MORET 4 JEF2.2

JEFF3.1

4516 4273 4457 4459

1.00427 1.00399 1.00474 1.00438 1.00607 1.00467 1.00469

1.00563 1.00492 1.00532 1.00691 1.00603 1.00609 1.00534

TRIPOLI-4.3

ENDF/BVI.4 1.00168 1.00167 1.00159 1.00458 1.00504 1.00536 1.00420

JEF2.2 1.00040 1.00128 1.00073 1.00172 1.00202 1.00178 1.00215

SCALE5.1 ENDF/B-VI.7 0.99829 0.99853 0.99861 0.99932 0.99959 0.99890 1.00009

* The real concentrations are close to the given values

71